Flute acoustics: measurement, modelling and design - School of ...

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134 CHAPTER 9. APPLICATIONS AND FURTHER DIRECTIONS Table 9.1: The relationship between the slide extension and the position of the stopper relative to the embouchure hole. Slide extension (mm) Stopper position (mm) 0.0 20.0 10.0 19.0 20.0 17.0 31.0 15.5 Tuning (cents) 130 120 110 100 90 80 70 60 50 40 30 D4 Eb4 E4 F4 F#4 G4 G#4 A4 Bb4 B4 C5 C#5 Note -1 octave loco +1 octave +2 octaves Figure 9.9: The predicted tuning of the Rudall & Rose flute with the tuning slide at 0.0 mm and the stopper at 20.0 mm. Terry McGee measured the size and position of the finger holes on this flute, but was unable to obtain precise measurements of the keyed holes. This is because the pins on old flutes are often corroded in, and the wood is shrunken, making the removal of the pins difficult and risky. The diameters of the keyed holes were therefore taken from a similar flute in private hands. The finger holes are all undercut conically, although no attempt was made to quantify the extent of undercutting. The top half of the bore of the left hand body joint was ovoid in shape, so the maximum and minimum diameters were measured and averaged in the model. The tapered elliptical embouchure hole was approximated by a cone with the same entry and exit areas. This flute has a particularly long tuning slide with a maximum extension of 31 mm. Due to the ‘patent head’ at the maximum slide extension the stopper is 15.5 mm from the embouchure hole. The positions of the stopper with the slide fully closed and at intermediate positions are given in Table 9.1. FluteCAD was used to predict the tuning of the Rudall & Rose flute in each of the configurations listed in Table 9.1. The results are shown in Figures 9.9–9.12. In each graph the tuning is given in cents relative to the equal tempered scale with the note A4 at 440 Hz. The mean tuning and standard deviation for each of the slide positions is shown in Figure 9.13. The flute has the best internal tuning (smallest standard deviation) with the slide at 10 mm and the stopper at 19 mm, however the tuning is far from optimised even in this configuration
9.2. EIGHT-KEY FLUTE BY RUDALL &ROSE 135 Tuning (cents) 90 80 70 60 50 40 30 20 10 0 -10 D4 Eb4 E4 F4 F#4 G4 G#4 A4 Bb4 B4 C5 C#5 Note -1 octave loco +1 octave +2 octaves Figure 9.10: The predicted tuning of the Rudall & Rose flute with the tuning slide at 10.0 mm and the stopper at 19.0 mm. Tuning (cents) 50 40 30 20 10 0 -10 -20 -30 -40 -50 D4 Eb4 E4 F4 F#4 G4 G#4 A4 Bb4 B4 C5 C#5 Note -1 octave loco +1 octave +2 octaves Figure 9.11: The predicted tuning of the Rudall & Rose flute with the tuning slide at 20.0 mm and the stopper at 17.0 mm.
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Flute acoustics: measurement, model
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To Renée iii
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vi I am grateful to my parents, Ros
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x 4.4 Conclusions and further direc
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2 CHAPTER 1. INTRODUCTION and the p
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12 CHAPTER 2. THEORY AND LITERATURE
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k = ω c and pressure given by p(x,
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338 APPENDIX C. QUANTIFYING MUSIC s
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340 REFERENCES Botros, A., Smith, J
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342 REFERENCES Kob, M. & Neuschaefe
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